0=-16t^2+21t+6

Solution for 0=-16t^2+21t+6 equation:

0=-16t^2+21t+6

We move all terms to the left:

0-(-16t^2+21t+6)=0

We add all the numbers together, and all the variables

-(-16t^2+21t+6)=0

We get rid of parentheses

16t^2-21t-6=0

a = 16; b = -21; c = -6;
Δ = b2-4ac
Δ = -212-4·16·(-6)
Δ = 825
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{825}=\sqrt{25*33}=\sqrt{25}*\sqrt{33}=5\sqrt{33}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-5\sqrt{33}}{2*16}=\frac{21-5\sqrt{33}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+5\sqrt{33}}{2*16}=\frac{21+5\sqrt{33}}{32}
$